Extended Data Fig. 2: Possible edge structures in ν = − 5/3.

(a) Hole-conjugate FQH states such as ∣ν∣ = 2/3, 5/3 states can be modeled by a Laughlin- like FQH state of holes within a bulk integer quantum Hall state, leading to a small strip of increased filling factor around the edge of the sample. This is shown schematically in panels a and c by plotting the filling factor of holes ν_h ≡ − ν at the boundary between a ν = − 5/3 and ν = − 1 state, where the relevant fractional edges measured in the experiment occur. The MacDonald model³⁴ of the resulting edge structure posits a downstream integer mode at the outermost edge of the sample, as well as an upstream (counter-propagating) fractional mode. (b) In real experiments, the two counter-propagating charged modes are rarely observed, but rather mix through the presence of inter-edge interactions, yielding a single effective charge-2e/3 mode propagating downstream, as well as an upstream charge-neutral mode, as explained by the Kane-Fisher-Polchinski model³⁵. (c) A sufficiently soft confining potential may make it energetically favorable to redistribute the charge in the system and create an additional strip of density ν_h = 4/3, introducing a set of two additional counter-propagating fractional edge modes: the Meir model⁴⁰. (d) In a real system, where these modes can also mix, the resulting mode structure may contain two downstream fractional-conductance modes as well as two upstream neutral modes. This scenario is consistent with the observation of multiple fractional conductance steps within the ν = − 5/3 state.